{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T18:15:49Z","timestamp":1761675349937},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":4884,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:p>In the present paper the story is told of the brief and far from tranquil encounter of L.E.J. Brouwer and A. Fraenkel. The relationship which started in perfect harmony, ended in irritation and reproaches.<\/jats:p><jats:p>The mutual appreciation at the outset is beyond question. All the more deplorable is the sudden outbreak of an emotional disagreement in 1927. Looking at the Brouwer\u2013Fraenkel episode, one should keep in mind that at that time the so-called<jats:italic>Grundlagenstreit<\/jats:italic>was in full swing. An emotional man like Brouwer, who easily suffered under stress, was already on edgewhen Fraenkel's book<jats:italic>Zehn Vorlesungen \u00dcber die Grundlegung der Mengenlehre<\/jats:italic>, [Fraenkel 1927] was about to appear.<\/jats:p><jats:p>With the<jats:italic>Grundlagenstreit<\/jats:italic>reaching (in print!) a level of personal abuse unusual in the quiet circles of pure mathematics, Brouwer was rather sensitive, where the expositions of his ideas were concerned. So when he thought that he detected instances of misconception and misrepresentation in the case of his intuitionism, he felt slighted. We will mainly look at Brouwer's reactions. since the Fraenkel letters have not been preserved.<\/jats:p><jats:p>The late Mrs. Fraenkel kindly put the Brouwer letters that were in her possession at my disposal. I am grateful to the Fraenkel family for the permission to use the material.<\/jats:p><jats:p>I am indebted to Andreas Blass for his valuable suggestions and corrections.<\/jats:p><jats:p>Abraham Fraenkel (then still called Adolf) was one of the first non-partisan mathematicians, if not the first, who developed a genuine interest in intuitionism.<\/jats:p>","DOI":"10.2307\/421057","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T07:14:28Z","timestamp":1146986068000},"page":"284-310","source":"Crossref","is-referenced-by-count":8,"title":["Brouwer and Fraenkel on Intuitionism"],"prefix":"10.1017","volume":"6","author":[{"given":"Dirk Van","family":"Dalen","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600006399_ref012","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-25900-9"},{"key":"S1079898600006399_ref009","unstructured":"[ Brouwer 1907] Brouwer L.E.J. , Over de grondslagen der wiskunde, Ph.D. thesis , Amsterdam."},{"key":"S1079898600006399_ref014","volume-title":"Lebenskreise. Aus den Erinnerungen eines J\u00dcdischen Mathematikers","author":"Fraenkel","year":"1967"},{"key":"S1079898600006399_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-42478-0"},{"key":"S1079898600006399_ref017","first-page":"145","volume":"1","author":"Dalen","year":"1995","journal-title":"Hermann Weyl's intuitionistic mathematics"},{"key":"S1079898600006399_ref020","doi-asserted-by":"crossref","first-page":"159","DOI":"10.2307\/2272955","article-title":"An intuitionistic completeness theorem for intuitionistic predicate logic","volume":"41","author":"Veldman","year":"1976","journal-title":"The Journal of Symbolic Logic"},{"key":"S1079898600006399_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/BF03024028"},{"key":"S1079898600006399_ref002","first-page":"10","article-title":"A. Fraenkel, Zehn Vorlesungen \u00dcber die Grundlegung der Mengenlehre","volume":"39","author":"Brouwer","year":"1930","journal-title":"Jahresbericht der Deutschen Mathematiker-Vereinigung"},{"key":"S1079898600006399_ref008","first-page":"785","article-title":"On the structure of perfect sets of points","volume":"12","author":"Brouwer","year":"1910","journal-title":"Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings of the section of Sciences"},{"key":"S1079898600006399_ref001","article-title":"Het intu\u00eftionisme bij de Franse wiskundigen","volume":"XI","author":"Bockstaele","year":"1949","journal-title":"Verhandelingen van de Koninklijke Vlaamse Academie van Wetenschappen, Letteren en Schone Kunsten van Belgi\u00eb"},{"key":"S1079898600006399_ref007","first-page":"855","article-title":"Intuitionistische Einf\u00dchrung des Dimensionsbegriffes","volume":"29","author":"Brouwer","year":"1926","journal-title":"Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings of the section of Sciences"},{"key":"S1079898600006399_ref005","volume-title":"Intuitionismus","author":"Brouwer","year":"1992"},{"key":"S1079898600006399_ref010","first-page":"203","article-title":"Intuitionistische Mengenlehre","volume":"28","author":"Brouwer","year":"1919","journal-title":"Jahresbericht der Deutschen Mathematiker-Vereinigung"},{"key":"S1079898600006399_ref016","doi-asserted-by":"publisher","DOI":"10.1007\/BF02400412"},{"key":"S1079898600006399_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-663-15741-0"},{"key":"S1079898600006399_ref003","first-page":"1","article-title":"Begr\u00dcndung der Mengenlehre unabh\u00e4ngig vom logischen Satz vom ausgeschlossenen Dritten. Zweiter Teil, Theorie der Punktmengen","volume":"XII","author":"Brouwer","year":"1919","journal-title":"Verhandelingen der Koninklijke Akademie van Wetenschappen te Amsterdam (Eerste Sectie)"},{"key":"S1079898600006399_ref004","first-page":"139","article-title":"Historical background, principles and methods of intuitionism","volume":"49","author":"Brouwer","year":"1952","journal-title":"South African Journal of Science"},{"key":"S1079898600006399_ref006","first-page":"1189","article-title":"Intuitionistische Betrachtungen \u00dcber den Formalismus","volume":"36","author":"Brouwer","year":"1928","journal-title":"Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings of the section of Sciences"},{"key":"S1079898600006399_ref015","first-page":"174","volume-title":"Verhandlungen des Dritten Internationalen Mathematiker-Kongresses in Heidelberg vom 8. bis 13 August 1904","author":"Hilbert","year":"1905"},{"key":"S1079898600006399_ref021","doi-asserted-by":"publisher","DOI":"10.1007\/BF02102305"},{"key":"S1079898600006399_ref018","volume-title":"Mystic, geometer, and intuitionist: L.E.J. 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Volume 1 \u2013 The Dawning Revolution","author":"Dalen","year":"1999"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600006399","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:36:38Z","timestamp":1707032198000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600006399\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["S1079898600006399"],"URL":"https:\/\/doi.org\/10.2307\/421057","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}